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Match List-I with List-II

List-IList-II
A is given matrix∣adj(adjA)∣\left\vert \text{adj}(\text{adj}A) \right\vert
(A) Order of A =2×2= 2 \times 2 and ∣A∣=3\left\vert A \right\vert = 3(I) 33
(B) Order of A =3×3= 3 \times 3 and ∣A∣=2\left\vert A \right\vert = 2(II) 11
(C) Order of A =4×4= 4 \times 4 and ∣A∣=1\left\vert A \right\vert = 1(III) 1616
(D) Order of A =2×2= 2 \times 2 and ∣A∣=4\left\vert A \right\vert = 4(IV) 44

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 3

Use ∣adj(adj A)∣=∣A∣(n−1)2|adj(adj\,A)| = |A|^{(n-1)^2}.

(A) n=2n=2: 31=33^1 = 3.

(B) n=3n=3: 24=162^4 = 16.

(C) n=4n=4: 19=11^9 = 1.

(D) n=2n=2: 41=44^1 = 4.

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